- Due to its current interest for the exchange-correlation potential in density functional theory, the long-standing question of the relation between first- and second-order density matrices is reopened. In particular, the approximation of perfect pairing is applied, the examples of H2 and the H2 dimer being used to motivate a more formal treatment of ( N 2) pairs. For the H2 dimer and the general case of ( N 2) pairs, the strong orthogonality constraint is invoked. A characteristic of the present treatment is that natural orbital and natural geminal expansions of first- and second-order density matrices respectively reduce from generally infinite to specifically finite sums. Their occupation numbers are calculated explicitly. The present treatment allows an approximation transcending Hartree-Fock theory to be exhibited between first- and second-order density matrices. 1995.